Line Equation-Slope-Distance-Midpoint-Y intercept Calculator

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Given (0, 20) and (12, 30)

calculate 8 items:

Calculate the slope and point-slope form:

GCF Calculation

Reduce numerator and denominator by the (GCF) of 10

Slope = (10/10)/(12/10)

Calculate the point-slope form :

y - y₁ = m(x - x₁)

y - 20 = 5/6(x - 0)

Calculate the line equation

Standard equation of a line is y = mx + b
where m is our slope
x and y are points on the line
b is a constant.

Rearrange the equation to solve for b
we get b = y - mx.
Use (0, 20) and the slope (m) = 5/6

b = 20 - (5/6 * 0)

b = 20 - (0/1.2)

Solve for b

This fraction is not reduced. Using our GCF Calculator, we see that the top and bottom of the fraction can be reduced by 120

Our reduced fraction is:

Build standard line equation

y = 5/6x + 20

Distance between the 2 points

D = Square Root((x₂ - x₁)² + (y₂ - y₁)²)

D = Square Root((12 - 0)² + (30 - 20)²)

D = Square Root((12² + 10²))

D = √(144 + 100)

D = √244

D = 15.6205

Midpoint between the 2 points

Midpoint = (6, 25)

Form a right triangle

Plot a 3^rd point (12,20)

Our first triangle side = 12 - 0 = 12

Our second triangle side = 30 - 20 = 10

Using the slope we calculated
Tan(Angle1) = 0.83333333333333

Angle1 = Atan(0.83333333333333)

Angle1 = 39.8056°

Since we have a right triangle
We only have 90° left
Angle2 = 90 - 39.8056° = 50.1944

Calculate the y intercept of our line

The y intercept is found by
Setting x = 0 in y = 5/6x + 20

y = 5/6(0) + 20

y = 20

Find the parametric equations for the line

Parametric equations are written as
(x,y) = (x₀,y₀) + t(b,-a)

Plugging in our numbers, we get

(x,y) = (0,20) + t(12 - 0,30 - 20)

(x,y) = (0,20) + t(12,10)

x = 0 + 12t

y = 20 + 10t

Calculate Symmetric Equations:

Plugging in our numbers, we get:

Plot these points on the Cartesian Graph:

Final Answers